Geodesic
Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 140-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the Hamiltonian H of an electron in a two-dimensional lattice of point potentials in a transverse magnetic field whose flux is rational. An expansion of H in a direct integral over a two-dimensional torus of the reciprocal lattice of operators described by finite-dimensional matrices is obtained. This expansion is used to investigate the structure of the spectrum of H, whose continuum eigenfunctions are found. 
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     title = {Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice},
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V. A. Geiler; V. A. Margulis. Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 140-149. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a12/

[1] Geiler V. A., Margulis V. A., TMF, 58:3 (1984), 461–472 | MR

[2] Dodonov V. V., Malkin I. A., Man'ko V. I., Phys. Lett., 51A:3 (1975), 133–134 | DOI

[3] Zak J., Phys. Rev., A134:6 (1964), 1602–1611 | DOI | MR

[4] Boon M. H., J. Math. Phys., 13:8 (1972), 1268–1285 | DOI | MR

[5] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 4, Mir, M., 1982, 428 pp. | MR

[6] Novikov S. P., DAN SSSR, 257:3 (1981), 538–543 | MR | Zbl

[7] Lyskova A. S., UMN, 36:5 (1981), 181–182 | MR

[8] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 740 pp. | MR | Zbl

[9] Gantmakher F. R., Teoriya matrits, 3-e izd., Nauka, M., 1967, 575 pp. | MR

[10] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1969, 368 pp. | MR | Zbl